where I = b[d.sup.3]/12, d is the beam depth, b is the beam width, l is the beam length, f is the natural frequency of the specimen, n is the mode of vibration
, [rho] is the density, A is the cross-sectional area, and [m.sub.1] = 4.73.
This component could be associated with the second mode of vibration
of the structure.
The band at 867 [cm.sup.-1] is due to the [v.sub.1]([B.sub.2u]) mode of vibration
and that at 747 [cm.sup.-1] is due to the [v.sub.2]([B.sub.2u]) mode.
Membership functions Linguistic terms Description and range of the linguistic terms name L1F1, L1F2, L1F3, L1F4 [fnf.sub.1 to 4] Low ranges of relative natural frequency for first mode of vibration
in descending order, respectively.
In the open circuit condition, the piezoelectric voltage [v.sub.i] due to the ith mode of vibration
and the global piezoelectric voltage v resulting from the modes superposition are
The computational analysis in the dynamic range consisted in determination of the first three frequencies of free vibrations and the corresponding mode of vibration
. The computations concerned the model of the spindle and the model of the spindle with spindle chuck and the representative workpiece.
On the other hand, any mode of vibration
with a frequency near or in phase to that of the rotation can lead to accelerated fatigue at points with stress concentration (such as point a).
The effect of vibration and the mode of vibration
on the acceleration of the relaxation process is well demonstrated in Refs.
By contrast, Hooke conceptualizes brain function in terms of a sounding bell, its mode of vibration
being quite different from that of a string.
Each mode of vibration
would correspond to information being stored in a particular way.
 studied to find the properties and also vibration response of a partially treated multilayer MR fluid beam and governing equations have been derived for partially treated multilayer prototype beam using finite element and Ritz method and compared the results with experimental and Ritz method; the effects of length and locations of MR fluid layers on the properties of the beam are investigated under different magnetic field conditions and demonstrated upon the boundary conditions and mode of vibration
to be controlled for the effective vibration suppression has been derived.
Analyzing Figure 3, it is very clear the presence of an active mode of vibration
around 571 [cm.sup.-1] and 601 [cm.sup.-1] corresponding to the O-P-O bonds of HA flexion type (v4) (Siriphannon et al., 2002).